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This link shows information, including a "zoom into" the detail of a subsection of a Weierstrass function. It stops, and the notes say that the limitations of the software used to analyze the values for f(x) are hitting the limits of (I'm guessing) the most precise floating point type on the system.

My question is: Is there any Python code that can create a "deep zoom" plot of a function and go beyond the limitations of the floating point type (even if it's very very slow)? What would I use? BigNum? Something else? I'm hoping someone has already made a "plot tool" that could analyze a Weierstrass function at a resolution finer than floating point math.

enter image description here

Since the function is an endless series, one would have to evalulate it up to X terms of the expression, and so the deeper you zoom in, the more terms would have to be evaluated. Secondly, if it is possible (by some careful work) to make a special case of an evalulator that plots the Weierstrass function shown above to any arbitrary precision without requiring specialized data types (that is, working within floating point limits) then that would also be pretty great.

Martin B
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Warren P
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2 Answers2

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Try gmpy, which is Python bindings to the GNU multiprecision library. It can handle the range "roughly 2^-68719476768 to 2^68719476736" on a 32 bit system.

Andrew Dalke
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Python's Decimal type will give you arbitrary precision floats. matplotlib will allow you to create plots.

setrofim
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